spain-selectividad 2021 QA.3

spain-selectividad · Other · selectividad__madrid_matematicas-II_extraordinaria 2.5 marks Vectors: Lines & Planes Multi-Step Geometric Modeling Problem
Given the point $A ( 1,0 , - 1 )$, the line $r \equiv x - 1 = y + 1 = \frac { z - 2 } { 2 }$ and the plane $\pi \equiv x + y - z = 6$, find:
a) ( 0.75 points) Find the angle formed by the plane $\pi$ and the plane perpendicular to the line $r$ that passes through point $A$.
b) ( 0.75 points) Determine the distance between the line $r$ and the plane $\pi$.
c) (1 point) Calculate an equation of the line that passes through A, forms a right angle with the line $r$ and does not intersect the plane $\pi$.
Given the point $A ( 1,0 , - 1 )$, the line $r \equiv x - 1 = y + 1 = \frac { z - 2 } { 2 }$ and the plane $\pi \equiv x + y - z = 6$, find:

a) ( 0.75 points) Find the angle formed by the plane $\pi$ and the plane perpendicular to the line $r$ that passes through point $A$.

b) ( 0.75 points) Determine the distance between the line $r$ and the plane $\pi$.

c) (1 point) Calculate an equation of the line that passes through A, forms a right angle with the line $r$ and does not intersect the plane $\pi$.